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We report on the impact of magnetoelastic coupling on the magnetocaloricproperties of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ in terms of the vibrationaldensity of states, which we determined with $^{57}$Fe nuclear resonantinelastic X-ray scattering measurements and with density-functional-theorybased first-principles calculations in the ferromagnetic low-temperature andparamagnetic high-temperature phase. In experiments and calculations, weobserve pronounced differences in the shape of the Fe-partial VDOS betweennon-hydrogenated and hydrogenated samples. This shows that hydrogen does notonly shift the temperature of the first-order phase transition, but alsoaffects the elastic response of the Fe-subsystem significantly. In turn, theanomalous redshift of the Fe VDOS, observed by going to the low-volume PMphase, survives hydrogenation. As a consequence, the change in the Fe specificvibrational entropy $\Delta S_\mathrm{lat}$ across the phase transition has thesame sign as the magnetic and electronic contribution. DFT calculations showthat the same mechanism, which is a consequence of the itinerant electronmetamagnetism associated with the Fe subsystem, is effective in both thehydrogenated and he hydrogen-free compounds. Although reduced by 50 % ascompared to the hydrogen-free system, the measured change $\DeltaS_\mathrm{lat}$ of 3.2\pm1.9 J/kgK across the FM to PM transition contributeswith 35 % significantly and cooperatively to the total isothermal entropychange $\Delta S_\mathrm{iso}$. Hydrogenation is observed to induce an overallblueshift of the Fe-VDOS with respect to the H-free compound; this effect,together with the enhanced Debye temperature observed, is a fingerprint of thehardening of the Fe sublattice by hydrogen incorporation. In addition, the meanDebye velocity of sound of LaFe$_{11.4}$Si$_{1.6}$H$_{1.6}$ was determined fromthe NRIXS and the DFT data.

physical review. b./physical review. b

Influence of hydrogenation on the vibrational density of states of  magnetocaloric  $\mathrm{LaFe}_\mathrm{11.4}\mathrm{Si}_\mathrm{1.6}\mathrm{H}_{1.6}$